Maxpool. Besides ReLU, Sigmoid, Arctan, and Tanh functions, Maxpool is a non-linear function commonly used in CNNs. However, as it is a multivariate function, Maxpool is far more complex to be verified. DeepPoly [1]} gives a loose linear bound to Maxpool and its parallel work, CNN-Cert [2]} gives non-trivial bounds by leveraging a hyperplane containing n different particular points. 3DCertify [3]} gives tighter bounds than DeepPoly by double description method and is appliable for point cloud models.
However, 3DCertify's perturbation form is rotation and is not suitable for image data, which is perturbed in a \(l_p\) -norm ball.
